Boundedness of commutators generated by m-th Calder\'on-Zygmund type singular integrals and local Campanato functions on generalized local Morrey spaces

Abstract

Let $T_m$ be the $m$-th Calder\'on-Zygmund type singular integral. In the paper, we consider the boundedness of $T_m$ on the generalized product local Morrey spaces $LM_{p_1,\varphi_1}^{\{x_0\}}\times LM_{p_2,\varphi_2}^{\{x_0\}}\times\dots\times LM_{p_m,\varphi_m}^{\{x_0\}}.$ And, the boundedness of the commutators of $T_m$ with local Campanato functions is obtained, also.